Synchronous Generator Load Sharing Calculation

This problem requires us to determine the individual power output of two synchronous generators connected in parallel. We are given their power ratings, the total load they are supplying, and the governor droop setting for both machines.

Understanding Governor Droop and Load Sharing

When synchronous generators operate in parallel, their governors regulate their power output based on the system frequency. The governor droop characteristic determines how much the power output changes for a given change in frequency. A droop setting means that as the load increases, the frequency typically decreases (or vice versa). Crucially, when multiple generators with the same droop percentage are synchronized and operating in parallel, they will naturally share the total system load in proportion to their individual capacity ratings. This ensures stable operation and appropriate distribution of the demand among the available resources.

Generator Specifications and Load Data

We have the following information provided:

Total Load Supplied by both generators: $300 \text{ MW}$

Governor Droop Setting for both G1 and G2: $4\%$

Calculating Individual Power Outputs

Since both generators share the same governor droop setting (4%), the total load of $300 \text{ MW}$ will be divided between them proportionally based on their installed capacities. First, we calculate the total capacity of the combined system.

Step 1: Calculate Total System Capacity

The total capacity is the sum of the individual ratings of the generators operating in parallel.

Total Capacity ($C_{total}$) = Rating$_{G1}$ + Rating$_{G2}$

Using mathematical notation:

$$C_{total} = R_1 + R_2$$

Substituting the given values:

$$C_{total} = 200 \text{ MW} + 400 \text{ MW}$$

$$C_{total} = 600 \text{ MW}$$

Step 2: Calculate Power Supplied by G1

Generator G1 will supply a portion of the total load that is equal to its rating relative to the total system capacity, multiplied by the total load.

Power Supplied by G1 ($P_{G1}$) = Total Load $\times \frac{\text{Rating}_{G1}}{\text{Total Capacity}}$

Using mathematical notation:

$$P_{G1} = P_{load} \times \frac{R_1}{C_{total}}$$

Substituting the values:

$$P_{G1} = 300 \text{ MW} \times \frac{200 \text{ MW}}{600 \text{ MW}}$$

$$P_{G1} = 300 \text{ MW} \times \frac{1}{3}$$

$$P_{G1} = 100 \text{ MW}$$

Step 3: Calculate Power Supplied by G2

Similarly, Generator G2 will supply a portion of the total load proportional to its rating relative to the total system capacity.

Power Supplied by G2 ($P_{G2}$) = Total Load $\times \frac{\text{Rating}_{G2}}{\text{Total Capacity}}$

Using mathematical notation:

$$P_{G2} = P_{load} \times \frac{R_2}{C_{total}}$$

Substituting the values:

$$P_{G2} = 300 \text{ MW} \times \frac{400 \text{ MW}}{600 \text{ MW}}$$

$$P_{G2} = 300 \text{ MW} \times \frac{2}{3}$$

$$P_{G2} = 200 \text{ MW}$$

Conclusion: Power Supplied by Each Generator

After performing the calculations based on the principle of proportional load sharing due to identical governor droop settings, we find that Generator G1 supplies $100 \text{ MW}$ and Generator G2 supplies $200 \text{ MW}$.

Thus, the individual power supplied by each generator is:

G1 = 100 MW, G2 = 200 MW